I suggest you post on the board at antiqueradios.com - someone there might know more. These Stromberg sets have lasted longer than most, 'cuz they're too heavy to move...
Does the motor have continuity on either winding? Is this a reversible motor? 24VAC motors shouldn't be hard to come by, or a DC gear motor could maybe be adapted to work here. I've never seen this set, so I'm guessing, though.